A residual-based bootstrap for functional autoregressions
Statistics Theory
2019-05-21 v1 Statistics Theory
Abstract
We consider the residual-based or naive bootstrap for functional autoregressions of order 1 and prove that it is asymptotically valid for, e.g., the sample mean and for empirical covariance operator estimates. As a crucial auxiliary result, we also show that the empirical distribution of the centered sample innovations converges to the distribution of the innovations with respect to the Mallows metric.
Cite
@article{arxiv.1905.07635,
title = {A residual-based bootstrap for functional autoregressions},
author = {Jürgen Franke and Euna Gesare Nyarige},
journal= {arXiv preprint arXiv:1905.07635},
year = {2019}
}